"We have looked at this thing from every which way," Thomas told the insider newsletter. "It doesn't make sense to get in. We don't see a chance to win. I don't want to be a second candidate against an incumbent."
His decision means Mourdock will likely have a clear shot against Lugar in the May primary. The state filing deadline is Feb. 21.
Thomas also said he would not endorse Lugar or Mourdock.
In 2010, Thomas spent $600,000 out of his own pocket to challenge then-Rep. Mark Souder (R-Ind.). Thomas lost his primary bid to Souder by about 14 points in what was a crowded GOP field.
Rep. Eric Swalwell, D-Calif., walks on Broadway after a Future Forum with young entrepreneurs in the Flatiron District of New York City, April 16, 2015. Reps. Steve Israel, D-N.Y., Seth Moulton, D-Mass., and Grace Meng, D-N.Y., also attended.